Nonlinear extended images via image-domain interferometry

Abstract

Wave-equation, finite-frequency imaging and inversion still face many challenges in addressing the inversion of highly complex velocity models as well as in dealing with nonlinear imaging ͑e.g., migration of multiples, amplitude-preserving migration͒. Extended images ͑EIs͒ are particularly important for designing image-domain objective functions aimed at addressing standing issues in seismic imaging, such as two-way migration velocity inversion or imaging/inversion using multiples. General oneand two-way representations for scattered wavefields can describe and analyze EIs obtained in wave-equation imaging. We have developed a formulation that explicitly connects the wavefield correlations done in seismic imaging with the theory and practice of seismic interferometry. In light of this connection, we define EIs as locally scattered fields reconstructed by model-dependent, image-domain interferometry. Because they incorporate the same one-and two-way scattering representations used for seismic interferometry, the reciprocity-based EIs can in principle account for all possible nonlinear effects in the imaging process, i.e., migration of multiples and amplitude corrections. In this case, the practice of two-way imaging departs considerably from the one-way approach. We have studied the differences between these approaches in the context of nonlinear imaging, analyzing the differences in the wavefield extrapolation steps as well as in imposing the extended imaging conditions. When invoking single-scattering effects and ignoring amplitude effects in generating EIs, the one-and two-way approaches become essentially the same as those used in today's migration practice, with the straightforward addition of space and time lags in the correlationbased imaging condition. Our formal description of the EIs and the insight that they are scattered fields in the image domain may be useful in further development of imaging and inversion methods in the context of linear, migration-based velocity inversion or in more sophisticated image-domain nonlinear inverse scattering approaches.

Controlled-source interferometric redatuming by crosscorrelation and multidimensional deconvolution in elastic media

“…Interferometry by multidimensional deconvolution as such can be compared with migration deconvolution (Hu et al, 2001;Yu et al, 2006;Zhang and Ulrych, 2010). Such an analogy is also pointed out by Vasconcelos et al (2010), who present an imaging condition for oneway wavefields that is very similar to equation 4. In migration, the PSF generally has to be obtained from a velocity model, whereas in interferometry it can be computed from actually measured Green's functions, allowing us to focus not only the direct arrival but instead focus the complete wavefield.…”

Retrieving Reservoir-only Reflection and Transmission Responses from Target-enclosing Extended Images

“…Retrieved from surface seismic data, extended images (EIs) can be thought of as local reflectivity responses of the subsurface, for pseudo-sources and receivers placed inside of the medium (Vasconcelos et al, 2010;Thomson et al, 2016). Here, we further extend this concept by defining the block system , (1) where the quantities involved are (Figure 1) , (2) (3) and (4).…”

“…1b), with pseudosources both on the top (denoted by R + and T + ) and bottom (Rand T -). In equation 1, the TEEIs are properties of the enclosed medium that take the input F in fields into the output F out : the matrix blocks P + and P -are, respectively, down-and up-going wavefield matrices (Vasconcelos et al, 2010;van der Neut et al, 2013) due to sources on the acquisition surface, observed either on the top or bottom datums, as indicated by the subscripts top and bot (Fig. 1a).…”

“…A key enabler for our objective is the novel approach of Marchenko redatuming (Wapenaar et al, 2014; van der Neut et al, 2015;Ravasi et al, 2016): it allows us to obtain, from surface reflection data, subsurface redatumed waves that correctly handle internal multiples, while using conventional migration models. Combining this with the concepts of target-enclosing interferometry (van der Neut et al, 2013) and Reflectivity-based extended images (Vasconcelos et al, 2010;Thomson et al, 2016) we propose the new Target-Enclosing Extended Images. Here, we present this new concept, discuss how to estimate the associated fields, and support our claims with a field data example.…”

Target-enclosed seismic imaging

“…By propagating wavefields backward in a detailed subsurface model, rather than in a smooth macro model, and crosscorrelating them with their associated source fields in the detailed model, we can image the primary reflections and internal multiples to improve seismic resolution (Youn and Zhou, 2001;Malcolm et al, 2009;Vasconcelos et al, 2010). Because internal multiples are used in this image, this strategy has also been referred to as nonlinear imaging (Fleury and Vasconcelos, 2012;Ravasi et al, 2014).…”